Question

Find the volume of a right circular cone with:

(i) radius 6 cm, height 7 cm.

(ii) radius 3.5 cm, height 12 cm

(iii) height 21 cm and slant height 28 cm.

Answer 1

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume =

(i) Substituting the values of r = 6 cm and h = 7 cm in the above equation and using

Volume =

= (22) (2) (6)

= 264

Hence the volume of the given cone with the specified dimensions is

(ii) Substituting the values of r = 3.5 cm and h =12 cm in the above equation and using

Volume =

= (22) (0.5) (3.5) (4)

= 154

Hence the volume of the given cone with the specified dimensions is

(iii) In a cone, the vertical height ‘h’ is given as 21 cm and the slant height ‘l’ is given as 28 cm.

To find the base radius ‘r’ we use the relation between r, l and h.

We know that in a cone

=

=

=

Therefore the base radius is, r = cm.

Substituting the values of r = cm and h = 21 cm in the above equation and using

Volume =

= (22) (343)

= 7546

Hence the volume of the given cone with the specified dimensions is